1. Field of the Invention
The present invention relates generally to an initial correction factor determining device applied to detection of the drop in air pressure of a tire, for example, for finding an initial correction factor for eliminating the effect of a relative difference in effective rolling radius, depending on an initial difference between tires, on the rotational velocity. Further, it relates to a slip factor calculating device applied to detection of a drop in air pressure of a tire, for example, for calculating the slip factor of a driving tire. Furthermore, it relates to a tire pressure drop detecting device for detecting a drop in air pressure of a tire utilizing the rotational velocity corrected using the initial correction factor found by the initial correction factor determining device.
2. Background Art
In recent years, as an example of a safety device of a four-wheel vehicle such as an automobile or a truck, devices for detecting a drop in air pressure of a tire have been developed, and some of them have been put to practical use.
An example of a method of detecting a drop in air pressure of a tire is a method utilizing the differences among the respective rotational velocities F.sub.1, F.sub.2, F.sub.3, and F.sub.4 of four tires W.sub.1, W.sub.2, W.sub.3, and W.sub.4 mounted on a vehicle. The tires W.sub.1 and W.sub.2 are right and left front tires. The tires W.sub.3 and W.sub.4 are right and left rear tires.
In this detecting method, the rotational velocity F.sub.i of each of the tires W.sub.i (i=1, 2, 3, 4) is detected for each predetermined sampling period on the basis of a signal outputted from a wheel speed sensor associated with the tire W.sub.i.
The detected rotational velocities F.sub.i are equal if all of the effective rolling radii of the respective tires W.sub.1 are the same, and the vehicle is traveling linearly. The effective rolling radius is the distance the tire W.sub.i freely rolling in a loaded state (rolling in a state where both the slip angle and the slip factor are zero) moves by one rotation divided by 2.pi..
On the other hand, the effective rolling radius of each of the tires W.sub.i changes with changes in air pressure in the tire W.sub.i, for example. That is, when the air pressure in the tire W.sub.i drops, the effective rolling radius thereof is smaller than that at a time of normal internal pressure. Consequently, the rotational velocity F.sub.i of the tire W.sub.i whose air pressure drops is higher than that at a time of normal internal pressure. Therefore, the reduced pressure of the tire W.sub.i can be judged on the basis of differences among the rotational velocities F.sub.i.
An equation used in detecting the drop in air pressure in the tire W.sub.i on the basis of differences among the rotational velocities F.sub.i is the following equation (1), for example (see Japanese Patent Laid-Open (KOKAI) No. 305011/1988, Japanese Patent Laid-Open (KOKAI) No. 212609/1992, etc.). ##EQU1##
If the effective rolling radii of the tires W.sub.i are the same, the respective rotational velocities F.sub.i are the same (F.sub.1 =F.sub.2 =F.sub.3 =F.sub.4). Consequently, the judged value D is zero. Therefore, threshold values D.sub.TH1 and D.sub.TH2 (where D.sub.TH1, D.sub.TH2 &gt;0) are set. When conditions indicated by the following expression (2) are satisfied, it is judged that there is a tire W.sub.i whose air pressure has dropped. When the conditions are not satisfied, it is judged that all the tires W.sub.i have normal internal pressure: EQU D&lt;-D.sub.TH1 or D&gt;D.sub.TH2 (2)
The effective rolling radii of the actual tires W.sub.i include variations within the production standard occurring at the time of fabricating the tires W.sub.i (hereinafter referred to as an "an initial difference"). That is, even if the four tires W.sub.i have normal internal pressure, the effective rolling radii of the four tires W.sub.i differ due to the initial difference. Correspondingly, the rotational velocities F.sub.i of the tires W.sub.i vary. As a result, the judged value D may be a value other than zero. Therefore, it is erroneously detected that the air pressure has dropped, although it has not dropped. In order to detect the drop in air pressure with high precision, therefore, it is necessary to eliminate the effect of the initial difference from the detected rotational velocity F.sub.i.
It is considered that as a technique for eliminating the effect of the initial difference from the rotational velocity F.sub.i, a technique disclosed in Japanese Patent Laid-Open (KOKAI) No. 271907/1992, for example, is applied. In the technique disclosed in this gazette, a vehicle is caused to travel linearly on a path at a predetermined speed, and any one of the rotational velocities F.sub.i of the tires W.sub.i detected at that time is used as a basis to find correction factors K.sub.i. When the rotational velocity F.sub.1 of the tire W.sub.1 is used as a basis, the correction factors K.sub.i are found by the following equations (3) to (6): EQU K.sub.1 =F.sub.1 /F.sub.1 (3) EQU K.sub.2 =F.sub.1 /F.sub.2 (4) EQU K.sub.3 =F.sub.1 /F.sub.3 (5) EQU K.sub.4 =F.sub.1 /F.sub.4 (6)
The rotational velocities F.sub.i detected at the time of normal traveling are respectively multiplexed by the correction factors K.sub.i. Consequently, the effect of the initial difference on the rotational velocity F.sub.i is eliminated to some extent.
When the vehicle is a front engine front drive vehicle (FF vehicle) or a front engine rear drive vehicle (FR vehicle), each of the correction factors K.sub.3 and K.sub.4 expressed by the foregoing equations (5) and (6) is the ratio of the rotational velocities of a driving tire and a following tire.
On the other hand, driving torque or braking torque (hereinafter abbreviated to as "driving/braking torque") is applied to the driving tire at the time of traveling. The torque may cause the driving tire to slip. Therefore, the rotational velocity F.sub.i of the driving tire is generally expressed by the following equation (7). In the following equation (7), Rs is the slip factor, V is the speed of the vehicle, and r.sub.i is the effective rolling radius of the tire W.sub.i : ##EQU2##
In the case of the FF vehicle, the tires W.sub.1 and W.sub.2 are driving tires, and the tires W.sub.3 and W.sub.4 are following tires, whereby the correction factor K.sub.3 can be expressed by the following equation (8) from the foregoing equations (5) and (7): ##EQU3##
The effect of the slip factor Rs is exerted on the correction factor K.sub.3 expressed by the ratio of the rotational velocities of the driving tire and the following tire. The same is true to the correction factor K.sub.4.
More specifically, the slip factor Rs is expressed by the following equation (9) until the tire W.sub.i reaches the grip limit: ##EQU4##
In the equation (9), .mu. is the coefficient of friction of a road surface, C.sub.X is the shear modulus of the tire W.sub.i, W.sub.D is the width of a grounding area, L is the length of the grounding area, and T is a driving/braking force. The driving/braking force T is approximately proportional to the square of the speed V of the vehicle at the time of constant-speed traveling.
Consequently, the correction factors K.sub.3 and K.sub.4 include the effects of the coefficient of friction .mu. of the road surface and the speed V of the vehicle at the time of a trial. At a time of actual (normal, not a trial) travel, however, the vehicle travels on road surfaces having various coefficients of friction .mu. at various speeds V. Even if the rotational velocities F.sub.i are corrected using the correction factors K.sub.3 and K.sub.4 found at a time of trial traveling, therefore, the rotational velocities cannot be accurately corrected. Accordingly, it is difficult to eliminate the effect of the initial difference from the rotational velocity F.sub.i with high precision.
When the vehicle travels around a corner or a curve (hereinafter represented by a "corner"), lateral acceleration is exerted on the vehicle. As a result, the load exerted on the vehicle is toward the outside of the corner. Consequently, the effective rolling radius of the tire W.sub.i on the inside of (facing) the corner is increased, and the ground contact area thereof is relatively decreased. On the other hand, the effective rolling radius of the tire W.sub.i on the outside of (facing away from) the corner is decreased, and the ground contact area thereof is relatively increased.
On the other hand, a driving force produced by the engine is almost equally applied to the tire W.sub.i on the inside of the corner and the tire W.sub.i on the outside of the corner by a differential gear. As a result, variations arise in the slip factor Rs between the tire W.sub.i on the inside of the corner and the tire W.sub.i on the outside of the corner. Therefore, variations arise in the rotational velocity F.sub.i between the tire W.sub.i on the inside of the corner and the tire W.sub.i on the outside of the corner.
Even if all the tires W.sub.i have normal internal pressure, therefore, the variations in the rotational velocity F.sub.i are created by the variations in the slip factor Rs at the time of cornering. As a result, the judged value D includes an error corresponding to the variations in the slip factor Rs, whereby the reduced pressure may not be accurately judged. In order to judge the reduced pressure with high precision, therefore, the effect of the slip factor Rs must be eliminated.
In order to eliminate the effect of the slip factor Rs, it is considered that a technique proposed in Japanese Patent Application No. 6-312123 previously filed by the present applicant is applied. In the proposed technique, the judged value D is corrected in the following manner.
A variation component .DELTA.D of the judged value D due to the variations in the slip factor Rs is proportional to a variation component .DELTA.Rs of the slip factor Rs. On the other hand, the variation component .DELTA.Rs of the slip factor Rs is proportional to lateral acceleration LA applied to the vehicle, and is inversely proportional to the turning radius R.
The slip factor Rs shall be defined by the following equation (10) until the tire W.sub.i reaches the grip limit: ##EQU5##
Furthermore, the driving/braking force T shall be proportional to the square of the speed V of the vehicle and front/rear acceleration FRA applied to the vehicle.
The variation component .DELTA.D of the judged value D can be expressed by the following equation (11) on the basis of the foregoing relationship, letting .alpha.1, .alpha.2 and .alpha.3 be proportional constants: ##EQU6##
The variation component .DELTA.D expressed by the equation (11) is taken as a correction factor, and the correction factor is subtracted from the judged value D found by the foregoing equation (1). Consequently, the effect of the slip factor Rs on the judged value D is eliminated.
In the proposed technique, the slip factor Rs is utilized upon being defined by the foregoing equation (10). However, the slip factor Rs is actually inversely proportional to the coefficient of friction .mu. of the road surface, as expressed by the foregoing equation (9). In the proposed technique, therefore, there are possibilities that the judged value D after the correction has a large error depending on the state of the road surface, and the effect of the slip factor Rs cannot necessarily be accurately eliminated from the judged value D.
In the above-mentioned proposed technique, the relationship between the amount of variation in the effective rolling radius of each of the front tires W.sub.1 and W.sub.2 and the amount of variation in the effective rolling radius of each of the rear tires W.sub.3 and W.sub.4 out of the variations in the effective rolling radii of the tires Wi due to load movement at the time of cornering, is not considered. This is based on the presumption that the amount of variation in the effective rolling radius of each of the front tires W.sub.1 and W.sub.2 and the amount of variation in the effective rolling radius of each of the rear tires W.sub.3 and W.sub.4 are the same.
However, the front axle weight and the rear axle weight actually differ from each other. The front axle weight is the load exerted on the front axle on which the front tires are mounted. The rear axle is the load exerted on the rear axle on which the rear tires are mounted. For example, when the engine is set on the front side of the vehicle, the front axle weight is heavier than the rear axle weight.
Therefore, the amount of the load movement on the front tire side and the amount of the load movement on the rear tire side at the time of cornering differ from each other. This is particularly significant in the case of an FF vehicle. As a result, the amount of the variation in the effective rolling radius of a front tire and the amount of the variation in the effective rolling radius of a rear tire, differ from each other.
In order to correct the judged value D with high precision, therefore, the difference in the amount of the load movement between a front tire and a rear tire at the time of cornering must be considered.